Problem: $ E = \left[\begin{array}{rrr}3 & 3 & 4\end{array}\right]$ $ F = \left[\begin{array}{rr}2 & 3\end{array}\right]$ Is $ E F$ defined?
Solution: In order for multiplication of two matrices to be defined, the two inner dimensions must be equal. If the two matrices have dimensions $( m \times  n)$ and $( p \times q)$ , then $ n$ (number of columns in the first matrix) must equal $ p$ (number of rows in the second matrix) for their product to be defined. How many columns does the first matrix, $ E$ , have? How many rows does the second matrix, $ F$ , have? Since $ E$ has a different number of columns (3) than $ F$ has rows (1), $ E F$ is not defined.